This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified param...This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified parameter-frequency w.Numerical experiments show that this class of atomic functions has good approximation properties,especially in the case of large gradients(Gibbs phenomenon).In this work,for the first time,the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis.Application of these basis functions is shown in the function approximation example.The procedure for determining the best frequencies,which gives the smallest approximation error in terms of the least squares method,is presented.展开更多
In this paper, equivalent surface impedance boundary condition （ESIBC）, which takes fractal parameters （D, G） into SIBC, is implemented in the 4-component 2-D compact finite difference frequency domain （2-D CFDFD...In this paper, equivalent surface impedance boundary condition （ESIBC）, which takes fractal parameters （D, G） into SIBC, is implemented in the 4-component 2-D compact finite difference frequency domain （2-D CFDFD） method to an- alyze the propagation characteristics of lossy circular waveguide with fractal rough surface based on Weierstrass-Mandelbrot （W-M） function. Fractal parameters’ effects on attenuation constant are presented in the 3 mm lossy circular waveguide, and the attenuation constants of the first three modes vary monotonically with scaling constant （G） and decrease as the fractal dimension （D） increasing.展开更多
This study investigates the application of miniature quantum references within small-scale optical atomic frequency standards,utilizing a diminutive^(87)Rb glass cell,dimensions of 6 mm×6 mm×6 mm,to establis...This study investigates the application of miniature quantum references within small-scale optical atomic frequency standards,utilizing a diminutive^(87)Rb glass cell,dimensions of 6 mm×6 mm×6 mm,to establish a quantum frequency standard.'By employing the transition spectrum from 5^(2)S_(1/2)F=2 to 5^(2)P_(3/2)F=3,this study successfully demonstrates the development of a compact rubidium atomic optical frequency standard via modulation transfer spectroscopy(MTS).Subsequent to frequency stabilization,the 780 nm clock laser exhibits a linewidth of 6.9 k Hz,and its out-of-loop short-term stability reaches4.1×10^(-13)@1 s,as confirmed through beat frequency analysis.This research not only provides a practical blueprint for the development of small optical atomic frequency standards but also lays down essential groundwork for future advancements in chip-level optical frequency standard technologies.展开更多
A low-thermal-noise,small-sized,monolithic crystalline whispering-gallery-mode cavity can achieve a compact laser frequency locking system.In this study,we propose generating a Fano resonance spectrum within the cryst...A low-thermal-noise,small-sized,monolithic crystalline whispering-gallery-mode cavity can achieve a compact laser frequency locking system.In this study,we propose generating a Fano resonance spectrum within the crystalline cavity to achieve frequency locking without the need for traditional modulation techniques,aiming to further simplify the locking system.By coupling a prism with the crystalline cavity,we generate a Fano transmission spectrum to serve as the error signal for laser frequency locking.Experimental results show that our method achieves a level of noise suppression comparable to the classical Pound-Drever-Hall technique,reducing laser frequency noise to near the thermal noise limit of the crystalline cavity.It enables us to suppress the laser frequency noise to below 1 Hz^(2)∕Hz in the offset frequency range of 103-105Hz and achieve a minimum noise of0.2 Hz^(2)∕Hz.We also analyzed various unique optical noises in the Fano locking technique and found that the primary factor limiting laser frequency noise in this work is still the inherent thermal noise of the crystalline cavity.Our results indicate that the proposed Fano locking technique has significant potential to simplify laser locking systems,enhance stability,and reduce overall power consumption and cost.展开更多
文摘This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified parameter-frequency w.Numerical experiments show that this class of atomic functions has good approximation properties,especially in the case of large gradients(Gibbs phenomenon).In this work,for the first time,the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis.Application of these basis functions is shown in the function approximation example.The procedure for determining the best frequencies,which gives the smallest approximation error in terms of the least squares method,is presented.
文摘In this paper, equivalent surface impedance boundary condition （ESIBC）, which takes fractal parameters （D, G） into SIBC, is implemented in the 4-component 2-D compact finite difference frequency domain （2-D CFDFD） method to an- alyze the propagation characteristics of lossy circular waveguide with fractal rough surface based on Weierstrass-Mandelbrot （W-M） function. Fractal parameters’ effects on attenuation constant are presented in the 3 mm lossy circular waveguide, and the attenuation constants of the first three modes vary monotonically with scaling constant （G） and decrease as the fractal dimension （D） increasing.
文摘This study investigates the application of miniature quantum references within small-scale optical atomic frequency standards,utilizing a diminutive^(87)Rb glass cell,dimensions of 6 mm×6 mm×6 mm,to establish a quantum frequency standard.'By employing the transition spectrum from 5^(2)S_(1/2)F=2 to 5^(2)P_(3/2)F=3,this study successfully demonstrates the development of a compact rubidium atomic optical frequency standard via modulation transfer spectroscopy(MTS).Subsequent to frequency stabilization,the 780 nm clock laser exhibits a linewidth of 6.9 k Hz,and its out-of-loop short-term stability reaches4.1×10^(-13)@1 s,as confirmed through beat frequency analysis.This research not only provides a practical blueprint for the development of small optical atomic frequency standards but also lays down essential groundwork for future advancements in chip-level optical frequency standard technologies.
基金National Natural Science Foundation of China(62305136,62035007,61805112)。
文摘A low-thermal-noise,small-sized,monolithic crystalline whispering-gallery-mode cavity can achieve a compact laser frequency locking system.In this study,we propose generating a Fano resonance spectrum within the crystalline cavity to achieve frequency locking without the need for traditional modulation techniques,aiming to further simplify the locking system.By coupling a prism with the crystalline cavity,we generate a Fano transmission spectrum to serve as the error signal for laser frequency locking.Experimental results show that our method achieves a level of noise suppression comparable to the classical Pound-Drever-Hall technique,reducing laser frequency noise to near the thermal noise limit of the crystalline cavity.It enables us to suppress the laser frequency noise to below 1 Hz^(2)∕Hz in the offset frequency range of 103-105Hz and achieve a minimum noise of0.2 Hz^(2)∕Hz.We also analyzed various unique optical noises in the Fano locking technique and found that the primary factor limiting laser frequency noise in this work is still the inherent thermal noise of the crystalline cavity.Our results indicate that the proposed Fano locking technique has significant potential to simplify laser locking systems,enhance stability,and reduce overall power consumption and cost.
